A model with private information is constructed that supports conventional arguments for a government monopoly in supplying circulating media of exchange. The model also yields predictions, including rate-of-return dominance of circulating media of exchange, that are consistent with observations from free banking regimes and fiat money regimes. In a laissez faire banking equilibrium, fiat money is not valued, and the resulting allocation is not Pareto optimal. However, if private agents are restricted from issuing circulating notes, there exists an equilibrium with valued fiat money that Pareto dominates the laissez faire equilibrium and is constrained Pareto optimal.